Would you rather?
Would you rather: Have 10% of £5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?
Problem
If you are working in the USA units then go to
Would you rather...
Be given $60 \%$ of $2$ pizzas or $26 \%$ of $5$ pizzas?
Have $10 \%$ of $ £5$ or $75 \%$ of $80$p?
Be bitten by $15 \%$ of $120$ mosquitoes or $8 \%$ of $250$ mosquitoes?
Skip using a rope which is $54 \%$ of $105$cm long, or $88 \%$ of $2.75$m long?
Sit in a traffic jam for $33 \%$ of $2$ hours or $44 \%$ of $1$hr $40$mins?
Make sure you explain your reasons clearly.
Perhaps you'd like to make up some of your own questions like these and send them to us.
Getting Started
It's hard to give hints to this problem but here are a few things to think about:
- Try estimating which you think will be the answer first
- Linking percentages to fractions often helps
Student Solutions
Marion at Tattingstone School and Aditya, who is from Bristol Grammar, both calculated these percentages carefully and came to sensible conclusions!
- Have 10% of £5 or 75% of 80p. 10% of £5 is 50p:
10% of £5 = (10/100) * 500 = 5000/100 = 50
and 75% of 80p is 60p. I'd rather have the latter. - Have 60% of 2 pizzas or 26% of 5 pizzas. 60% of 2 is 1.2 and 26% of 5 is 1.3. Again, I'd rather have the latter.
- Get bitten by 15% of 120 mosquitoes or by 8% of 250 mosquitoes. 15% of 120 is 18 and 8% of 250 is 20. I'd prefer the first.
- Skip with a rope 54% of 105cm long or with one 88% of 2.75m long. 54% of 105cm is 56.7cm, and 88% of 2.75m is 2.42m = 242cm. I'd prefer using the longer rope.
- Get stuck in a traffic jam lasting 33% of 2 hours or 44% of 1 hr 40 mins. 33% of 120 minutes is 40 minutes, and 44% of 100 minutes is 44 minutes. I'd prefer neither!
Teachers' Resources
Would You Rather?
If you are working in the USA units then go to
Would you rather...
Be given $60 \%$ of $2$ pizzas or $26 \%$ of $5$ pizzas?
Have $10 \%$ of $ £5$ or $75 \%$ of $80$p?
Be bitten by $15 \%$ of $120$ mosquitoes or $8 \%$ of $250$ mosquitoes?
Skip using a rope which is $54 \%$ of $105$cm long, or $88 \%$ of $2.75$m long?
Sit in a traffic jam for $33 \%$ of $2$ hours or $44 \%$ of $1$hr $40$mins?
Make sure you explain your reasons clearly.
Perhaps you'd like to make up some of your own questions like these and send them to us.
Why do this problem?
Possible approach
Having given them a suitable length of time to work on the problems, bring everyone together. You could take a vote on each one to start with and then ask one group to explain how they came to that conclusion. Invite other groups to contribute different ways of working out the solution as well so that a range of methods are discussed.
You could then ask each group to make up their own question in a similar style which they could write on the blank card. These could then be swapped. Of course the group which poses the problem must have also worked out the solution!
Key questions
Possible extension